Data-adaptive Estimation in Longitudinal Data Structures with Applications in Vaccine Efficacy Trials

Abstract

This dissertation develops methodology for data-adaptive estimation of parameters defined on longitudinal data structures, while this abstract serves as an introduction to the material covered herein. The dissertation is organized into three related, but distinct chapters. Each chapter considers a similar data structure, wherein subjects are enrolled and followed over a period of time to obtain additional measurements, for example their failure status. During this followup period, subjects may drop out and therefore researchers are unable to observe the entire study population at all time points. Using the observed data, this dissertation develops asymptotically efficient estimators that may draw valid inferences on the original study population. Data from preventive vaccine trials serve as the motivation for much of the work in this dissertation. In such trials, subjects are randomized to receive an active vaccine or placebo vaccine and are subsequently followed over some period of time to ascertain infection status. This infection data may be augmented with pathogen genetic data. Scientific interest may lie in assessing the vaccine's efficacy to prevent infections of a certain genotype; this problem is considered in Chapter 1. Researchers may possess additional information on the expected incidence of an infection in the population under study. For example, such information may be ascertained from previous studies in the same population. In Chapter 2, we show how this information may be included in the estimation procedure to improve performance. The third and final chapter explores the construction of estimators that enjoy the unique property of being robust to model misspecification in terms of both estimation and inference drawn from the estimator.